WO2020118392A1

WO2020118392A1 - Method for compensating chromatic dispersion in band-limited digital signals

Info

Publication number: WO2020118392A1
Application number: PCT/BR2019/050188
Authority: WO
Inventors: Alexandre FELIPE
Original assignee: FUNDAÇÃO CPQD - Centro de Pesquisa e Desenvolvimento em Telecomunicações
Priority date: 2018-12-14
Filing date: 2019-05-23
Publication date: 2020-06-18
Also published as: BR102018076057A2

Abstract

The present invention describes a novel method for compensating chromatic dispersion in band-limited digital signals applied to optical-fibre communication systems with long-distance, high-symbol-rate connections, that are subject to distortion caused by the propagation of communication signals and require compensation of the dispersion, that is intended to reduce the complexity of the chromatic dispersion compensation, taking advantage of the particular shape of the second-order dispersion filter.

Description

METHOD FOR COMPENSATING CHROMATIC DISPERSION IN SIGNS

LIMITED BAND DIGITAL

[001] The present invention deals with a new method for compensation of chromatic dispersion in digital signals of limited band, applied to communication systems by optical fibers with long distance connections and high symbol rates, which present distortion due to the propagation of signals and require dispersion compensation, which aims to reduce the complexity of chromatic dispersion compensation, taking advantage of the particular shape of the second order dispersion filter.

FIELD OF THE INVENTION

[002] The method for compensation of chromatic dispersion in limited band digital signals, object of the present invention, is applied to communication systems by optical fibers with long distance connections and high symbol rates, which present distortion due to the propagation of signals and need dispersion compensation.

OBJECTIVE OF THE INVENTION

[003] The main objective of the method for compensating chromatic dispersion in limited band digital signals, the object of the present invention, is to reduce the complexity of chromatic dispersion compensation, taking advantage of the particular shape of the second order dispersion filter, by instead of employing a generic filtering technique.

[004] PROBLEM TO BE SOLVED

Dispersion is a distortion that occurs during the propagation of communication signals. In optical fiber communications, this effect is called chromatic dispersion, and in long distance connections and high symbol rates, this dispersion can reach thousands of samples. The chromatic dispersion can be compensated in the optical domain by means of special fibers (DCF - From English Dispersion Compensating Fiber) or in the digital domain using a time-invariant filter.

[005] The dispersion compensation performed through the digital domain using a time-invariant filter is widely used because it is viable and reduces deployment costs of the system as a whole. However, in some cases, this compensation for dispersion in the digital domain is very complex.

[006] The algorithm known today as FFT (from the English Fast Fourier Transform), became popular after the publication of the work AN ALGORITHM FOR THE MACHINE CALCULATION OF COMPLEX FOURIER SERIES, by James W. Cooley and John W. Tukey (1965), in which the time decimation variant of the FFT algorithm is presented. Among the many applications of this algorithm, we highlight filtering here.

[007] Thus, the present invention aims to reduce the complexity of chromatic dispersion compensation, taking advantage of the particular shape of the second order dispersion filter, allowing chromatic dispersion compensation by applying only one Fourier transformation, instead of two as is done in the current technique.

TECHNICAL STATUS

[008] There are some articles, patent documents and literature that describe filters, filtering methods and chromatic dispersion compensation methods through the digital domain using filters, however, none of these documents anticipates the method proposed here. Among these documents, the following can be highlighted:

[009] The work “ALGORITHM FOR THE MACHINE CALCULATION OF COMPLEX FOURIER SERIES”, by James W. Cooley and John W. T ukey (1965) in which the time decimation variant of the FFT algorithm (from English Fast Fourier) is presented Transform);

[010] The article by Tomas J. Stockham, Jr „“ HIGH-SPEED CONVOLUTION AND CORRELATION ”, 1966, presents a technique for calculating convolutions using the fast Fourier transform. In the same article, he suggests a signal slicing technique to calculate FFTs in blocks of a size similar to the smallest of the lengths of the operands. Technique that later becomes identified as an overlap-add;

[01 1] The book “THE DISCRETE-TIME SIGNAL PROCESSING” by Allan V. Oppenheim and Ronald W. Schafer mentions two main techniques for filtering long strings using fixed-size convolutions. The overlap-add technique consists of selecting juxtaposed slices of the data and filtering them individually, and adding the overlapping results after filtering. The overlap-save technique consists, in turn, of using slices of the input data with overlap, and taking advantage of some samples of the calculated convolution, which correspond to juxtaposed slices of the output;

[012] US patent document 2010/0196009 A1, “POLARIZATION INDEPENDENT FREQUENCYDOMAIN EQUALIZATION (FDE) FOR CHROMATIC DISPERSION (CD) COMPENSATION IN POLMUX COHERENT SYSTEMS", which describes the chromatic dispersion compensation in the time domain, using a universal architecture finite response time invariant filtering;

[013] US patent document 8,792,189 B1, “OPTIMIZED CHROMATIC DISPERSION FILTER’, which describes a system for chromatic dispersion filtering, in which the number of taps of the filter is truncated, removing tapes of lesser magnitude;

[014] Patent document WO 2016/095942 A1, “CHROMATIC DISPERSION COMPENSATION FILTER”, which describes a system supported by the convolution theorem; in this system, STFT (Short-Time Fourier Transform) is used, which consists of calculating the Fourier transform for slices of a signal and reconstructs the signal using overlap-save or overlap-add;

[015] The US patent document 7,649,927 B, “EQUALIZER FILTER WITH DYNAMICALLY CONFIGURABLE CONVOLUTION FILTER’, which describes a system that uses the same filtering strategy proposed by Stockham, only addressing some practical issues with concern for flexibility. And this system can be used to compensate for chromatic dispersion;

[016] Algebraic manipulations similar to those employed in this invention were used by Lawrence R. Rabiner, Ronald W. Schafer and Charles M Rader, in their work “THE CHIRP Z-TRANSFORM ALGORITHM AND ITS APPLICATIONS”, from 1968, to numerically calculate the z transform. of points in an exponential spiral on the complex plane. In this work, it is shown how the use of the z transform for various points can be obtained through a simple convolution;

[017] The work of Lawrence et al, is closely linked to the work of Leo I. Bluestein, entitled “A LINEAR FILTERING APPROACH TO THE COMPUTATION OF DISCRETE FOURIER TRANSFORM ”, from 1970. In this work, it is shown how an FFT of arbitrary size can be obtained by means of a convolution which, in turn, can be made using the FFT algorithm (of greater length, but a power of 2, is computed more efficiently);

[018] The article “CHROMATIC DISPERSION COMPENSATION USING DIGITAL UR FILTERING WITH COHERENT DETECTION”, by Giliad Condfarb and Guifang Li presents a different approach in essence to those mentioned so far. It consists of compensating for chromatic dispersion, using an infinite response filter that approximates the response of the chromatic dispersion filter using a much smaller number of coefficients. The filter is infinite response, and is implemented as a filter of real coefficients, a technical difficulty of this technique is that it requires an infinite response filter of the signal reversed in time;

[019] Fumio Koyama's article, Kenichi Iga, entitled “FREQUENCY CHIRPING IN EXTERNAL MODULATORS”, 1988, discusses how to modulate the phase together with the amplitude, influences the minimum possible pulse width as a function of distance and a parameter of gorgeio; and

[020] The article by AH Gnauck, SK Korotky, JJ Veselka, J. Nagel, CT Kemmerer, WJ Minford and DT Moser, entitled “DISPERSION PENALTY REDUCTION USING AN OPTICAL MODULATOR WITH ADJUSTABLE CHIRP", is experimentally evaluated for the effect of the gorgeio on the transmission using a modulator with the adjustable gorgeio parameter.

DESCRIPTION OF THE FIGURES

[021] Below, reference is made to the figures accompanying this descriptive report, for better understanding and illustration, where it can be seen:

[022] Figure 1 shows the scheme that can be used to implement the proposed filtering technique. Initially the signal: (1) goes through a resampling; (2) is multiplied by a gorge; (3) undergoes a Fourier transform; (4) is multiplied by a second gorge; (5) is resampled to the desired sample rate. [023] Figure 2 shows how the scheme can be adapted to correct a positive or negative amount of dispersion by conjugating (or not) the signal before and after filtering; and a multiplexer that allows you to choose the filtered signal or the original signal; thus, three different dispersion values can be compensated with this arrangement.

[024] Figure 3 shows how two blocks, one carrying an FFT of size N and the other carrying an FFT of size N / 4, can be connected to obtain 3 possible filters, without considering resampling.

[025] Figure 4 shows side by side equivalence relationships that can be used to simplify different projects.

GENERAL DESCRIPTION OF THE INVENTION

[026] The chromatic dispersion filter has a frequency response

Where K ₂ is the group velocity dispersion parameter related to the fiber chromatic dispersion parameter defined according to

Where l is the central wavelength of the channel, D = CL is the chromatic dispersion accumulated along the fiber, C is a characteristic parameter that depends on the type of fiber and ₀ is the speed of light.

The impulse response of the chromatic dispersion filter in the time domain is

[027] The time response is the conjugate complex of the frequency response multiplied by some constant. This model is valid if the signal has infinite bandwidth. When introducing bandwidth limitation in the signal with a rectangular window, the response in time is multiplied by a signal with the largest fraction of energy concentrated in a short time, whose magnitude approaches a rectangle when the K ₂ is large. [028] Limiting the signal with a rectangular band in time causes an analogous effect in the frequency domain. Throughout this description, we will refer to the signal with a rectangular window as the analytical form and its dual signal as a limited signal. // (ío) multiplied by a rectangular window is the frequency analytical response, the inverse Fourier transformation, is the time limited response, h (t) multiplied by a rectangular window is the analytical response in time, the Fourrier transformation of that signal is the frequency-limited response.

[029] Considering a response over time, normalized, and sampled so that

And a window of size N, the sampling period can be chosen so that

Explicitly

The output y _n , the convolution between an input signal x and the filter h can be calculated as

[030] Considering a window from - N / 2 to (N / 2 - 1), the summation outputs coincide for different values of n, with the discrete Fourier transform, so they can be calculated using the FFT algorithm.

[031] But as in the case of Stockham filtering, when using FFT, the indices are added to a cyclic group of N elements. Which means that the convolution will be calculated assuming periodic extensions of x and h. But it is worth noting that low frequency components are represented mainly by the filter samples close to the source. Therefore, if the signal x has a limited bandwidth, the terms for large values of (n - k) will have little influence on filtering. Leaving this premise, it is possible that, at least a slice of the FFT, will serve as a good approximation of the output y.

[032] More explicitly, a Fourier transform of size N can be used to compensate for the group velocity dispersion parameter, k ₂ = ± NT / 4p.

DETAILED DESCRIPTION AND FORM OF CARRYING OUT THE INVENTION

[033] Next, a preferred non-restrictive form of realization of the present invention, object of this patent, is described, where the configuration and application can vary in the appropriate form for each desired application; describing the constructive possibilities that lead to concretizing the described object and the way it works.

[034] In one of the embodiments of the invention, the signal is processed according to that shown in figure 1. Possibly, using a resampling before and another after filtering. In the resampling process, size N slices are created, extracted from the signal by copying N samples displaced N / 2 between them. The gorgeio produces a

; p (h-ΐ

sign that for the nth sample of a block is W ^J «; Of the FFT output, only N / 2 coefficients are considered from the N / 4 coefficient; Unused coefficients can be removed even before multiplying the output by the gorge, thus reducing the complexity of the system.

[035] Resampling can be done at a fixed rate, or a configurable system with a buffer to maintain the continuity of the data flow.

[036] In another embodiment, two control signals are used, allowing the block to compensate for 3 dispersion values ± LGG ₅ ² / 4p or 0. The Fourier transform could also be modified to change the compensation signal performed.

[037] Another realization combines two instances, one capable of compensating iVT _s ² / 4p, with a FFT of size N, and the other being able to compensate ± LGG ₅ ² / 16p or zero, by means of an FFT of size N / 4.

[038] In another embodiment, the filters of size N _lt N ₂ , N ₃ , ..., N _F are cascaded, each being able to compensate for -N _f Ts / 4n, 0 or N _f Ts / 4n, so that the compensation of all the concatenated filters is the sum of the compensation of each filter. In particular, the lengths can be chosen so that _{+ 1} = 3 N _t , this allows to compensate any amount of dispersion in a grid of equally spaced --N ₁ T ^2/4 Pa

3 ^f —1

+ - ^ - N ₁ T _s ² / 4n. In addition, this grid can be moved by cascading other filters.

[039] The frequency range is defined as y (t) = exp (l) · F ² t ² ) u (t) and the factor resampling is defined as y (t) = u (t / F). The complex conjugation to resampling and multiplication by gorgeio can be simplified when they appear consecutively and, in figure 4, several equivalence relations are shown that can be used in order to group similar elements and, therefore, can be simplified, giving rise to several possible new achievements.

[040] Thus, as described above, it can be noted that the method, object of the present invention, advantageously reduces the complexity of the chromatic dispersion compensation, being a new method for the state of the art by coating of unprecedented conditions of innovation, inventive activity and industrialization, which make it deserve the privilege of an invention patent.

Claims

1 - METHOD FOR COMPENSATION OF CHROMATIC DISPERSION IN LIMITED BAND DIGITAL SIGNS, method for compensation of chromatic dispersion in an optical communication system, where the signal: (1) is sliced into blocks of size N, which may be partially overlapped; (2) is multiplied by a gorge; (3) undergoes a Fourier transform; (4) is multiplied by a second gorge; (5) slices from the output blocks are combined to form the output signal; characterized by the filtering of the signal in the digital domain, using a second-order time-varying dispersion filter, through a single FFT to compensate for the group velocity dispersion parameter related to the fiber chromatic dispersion parameter.

2 - METHOD FOR COMPENSATION OF CHROMATIC DISPERSION IN LIMITED BAND DIGITAL SIGNS, method for compensation of chromatic dispersion in an optical communication system, according to claim 1, characterized by using a resampling before and after filtering, creating size N slices, extracted from the signal by copying N consecutive samples, which can be performed at a fixed rate, or in a configurable system with a buffer to maintain the continuity of the data flow.

3 - METHOD FOR COMPENSATION OF CHROMATIC DISPERSION IN LIMITED BAND DIGITAL SIGNS, method for compensation of chromatic dispersion in an optical communication system, according to claim 1, characterized by using control signals that allow to configure a system, using or not the combination of the input and the output to compensate for a positive or negative dispersion value, and use a multiplexer to select the filtered input or not; thus allowing to select three different dispersion compensations.

4 - METHOD FOR COMPENSATION OF CHROMATIC DISPERSION IN LIMITED BAND DIGITAL SIGNS, method for compensation of chromatic dispersion in an optical communication system, according to claim 1, characterized by filters of size N _lt N ₂ , N ₃ ,. .., N _F be cascaded, each being able compensate for negative dispersion ^, 0 or positive dispersion ^, so that the compensation of all the concatenated filters is the sum of the compensation of each filter.

5 - METHOD FOR COMPENSATION OF CHROMATIC DISPERSION IN LIMITED BAND DIGITAL SIGNS, method for compensation of chromatic dispersion in an optical communication system, according to claim 4, characterized by using control signals so that each of the filters can operate as a chromatic dispersion filter with coefficient -N _f T? / 4n, 0 or + N _f T ^ / 4n, thus allowing up to 3 ^F configurations.

6 - METHOD FOR COMPENSATION OF CHROMATIC DISPERSION IN LIMITED BAND DIGITAL SIGNS, method for compensation of chromatic dispersion in optical communication system, according to claim 5 characterized by choosing the parameters so that N _{i + 1} = 3 N _t compensate amounts of chromatic dispersion with equally spaced coefficients.

7 - METHOD FOR COMPENSATION OF CHROMATIC DISPERSION IN LIMITED BAND DIGITAL SIGNS, method for compensation of chromatic dispersion in an optical communication system, according to claim 5, characterized by combining configurable filters and non-configurable filters.

8 - METHOD FOR COMPENSATION OF CHROMATIC DISPERSION IN LIMITED BAND DIGITAL SIGNS, method for compensation of chromatic dispersion in an optical communication system, according to claim 6, characterized by employing listed equivalence relations to eliminate certain blocks from the final system.